Definition:Extension Problem
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Definition
Let $H$ and $K$ be groups.
The extension problem is to determine all groups $G$ such that:
- $K \trianglelefteq G$
- $G / K \cong H$
where:
- $K \trianglelefteq G$ denotes that $K$ is a normal subgroup of $G$
- $G / K$ denotes the quotient group of $G$ by $K$
- $\cong$ denotes group isomorphism.
Sources
- 1978: John S. Rose: A Course on Group Theory ... (previous) ... (next): $1$: Introduction to Finite Group Theory: $1.7$